Real numbers

Number Theory Level 1

Without actual division find out which of the following rational numbers has a terminating decimal expansion

P) $\frac { 17 }{ 90 }$

Q) $\frac { 33 }{ 50 }$

R) $\frac { 121 }{ { 2 }^{ 2 }\times { 5 }^{ 3 } }$

S) $\frac { 121 }{ { 2 }^{ 3 }\times { 3 }^{ 2 }\times { 7 }^{ 5 } }$

Q) and S) P) , Q) and R) Q) and R) Q) , R) and S)

1 solution

Dhaval Furia
May 31, 2014

The fraction is terminating if denominator is of the form (2^a)x(5^b) where a and b are non-negative integers. That is if the prime factorization of the denominator consists of only 2 and/or 5, the fraction after converting into decimal will terminate at some place.

Hey the rating is too high for this problem ..............

ashutosh mahapatra - 7 years ago

It has come down now..

Shabarish Ch - 6 years, 5 months ago

Real numbers

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